The Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO), together with its international partners Virgo and KAGRA, aim to directly observe gravitational waves emitted by astrophysical sources such as coalescencing of black hole and neutron star binary systems. The installation of the Advanced LIGO detectors is completed, and commissioning towards the first observation run is ongoing. Preliminary astrophysical data is expected in 2015. The sensitivity of those advanced gravitational-wave detectors in the observation band is limited by the quantum noise of light and the thermal noise associated with mirror coatings. A contributor to the thermal noise, expected to dominate in future cryogenic gravitational-wave detectors, is thermo-optic noise. It is caused by dissipation through thermal diffusion. The same physics also leads to an intensity noise coupling, known in art literature as photo-thermal effect.
The desire to lower the quantum noise in the gravitational-wave observation band has driven the power circulating in the Advanced LIGO arm cavities up to about 800 kW. The high laser power, in turn, couples the angular suspension modes of the two cavity mirrors. This Sidles-Sigg instability creates a soft (unstable) and a hard mode, whose frequency increases with the intra-cavity power. The detector's angular control system must control the soft and damp the hard mode, and at the same time must not contaminate the observation band, starting at 10 Hz in the case of Advanced LIGO.
Future gravitational wave detectors aim to extend the observational band to even lower frequencies, further aggravating this limitation. A model to overcome the angular instabilities has been proposed, based on a dual-carrier optical spring scheme demonstrated by the LIGO laboratory. The proposed angular trap setup uses two dual-carrier beams to illuminate two suspended optical cavities which share a single end mirror. However, the proposed angular trap set up suffers from instability as a result of the photo-thermal feedback. Accordingly, there exists a need in the art for a single-carrier optical spring that will not suffer from instability as a result of photo-thermal feedback.